The fifth term of a geometric sequence is 32 and the eighth term is 4. (a) Find the ratio. (2 marks) (b) Find the first term. (2

Question

The fifth term of a geometric sequence is 32 and the eighth term is 4.
(a) Find the ratio. (2 marks)
(b) Find the first term. (2 marks)
(C) Find the sum of the first 50 terms of the sequence. (3 marks)
What is the first term?

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Sigridomena 5 years 2021-07-21T01:28:03+00:00 1 Answers 109 views 1

Answers ( )

  1. nguyetanh
    0
    2021-07-21T01:29:47+00:00
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    Answer:

    a. 1/2

    b. 512

    c. 1024

    Step-by-step explanation:

    The nth term of a geometric progression can be written as;

    Tn = ar^n-1

    where a is the first term, r is the common ratio and n is the term number

    From the question;

    Fifth term = ar^4 = 32

    Eight term = ar^7 = 4

    a. We want to find the common ratio

    What to do here is that we can divide the 8th by the 5th term

    ar^7/ar^4 = 4/32

    r^3 = 1/8

    r^3 = (1/2)^3

    Thus r = 1/2

    b. First term

    we can make a substitution in any of the two given terms

    Let’s use the fifth term

    ar^4 = 32

    a * (1/2)^4 = 32

    a * 1/16 = 32

    a = 16 * 32

    a = 512

    C. Sum of the first 50 terms

    To calculate this, we use the sum of terms formula

    Sn = a(1- r^n)/1-r

    a = 512 , n = 50 and r = 1/2

    Making the substitution;

    Sn = 512(1-(1/2)^50)/1-1/2

    Kindly note that (1/2)^50 will be infinitesimally small and will be close to zero

    So we can approximate (1/2)^50 to be zero

    Hence;

    Sn = 512(1-0)/0.5

    Sn = 512/0.5

    Sn = 1024

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